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Proof step 6 from proof add-ones-grlen (previous step)

# bits = n + 1 + # bits1, # bits1 < # bits ⊦ bits = [], bitsand(bits, true ' + bits1) = (true ' + mklist(true, n)) + bits1, false ∈ bits

User applied rule induction

And obtained the following new goals

Proof step 7:
# bits = n + 1 + # bits1 ∧ # bits1 < # bits, ∀ bits0, bits, n. # bits0 < # bits1 → # bits = n + 1 + # bits0 ∧ # bits0 < # bits → bits = [] ∨ bitsand(bits, true ' + bits0) = (true ' + mklist(true, n)) + bits0 ∨ false ∈ bits ⊦ bits = [] ∨ bitsand(bits, true ' + bits1) = (true ' + mklist(true, n)) + bits1 ∨ false ∈ bits

Rule argument

indvar: # bits1 wfpred: <

Additional information

Used simplifier rules: <; (wellfounded) Used terms: # bits1